If \(p\)  is a polynomial,
the Julia set of \(p\)  is compact
and \(I(p)\)  is an open connected subset of \({\mathcal {F}}(p)\) ;
moreover, it is simply-connected if and only if \({\mathcal {J}}(p)\)  is connected.
This property is equivalent to the relation
\({\mathcal {C}}(p)\cap I(p)=\emptyset \) 
[1]}.
